The Greek god Ares is essentially what you're describing. Ares embodied to some degree the courage needed to fight a war, but to the Greeks he embodied all the worst aspects of war, dishonorable acts, chaos (which is the worst thing anyone can embody in the Hellenic worldview,) destruction, cruelty, etc. and thus they were ambivalent about him at best, at least in the intellectual class, whereas Athena is the Goddess of War and Wisdom and embodies all the noble and intellectual aspects of war.
It should come as no surprise that the people of Athens chose Athena as their patron deity over a god like Ares.
That's not even touching on the nature/nurture debate (last I checked the majority of people diagnosed as psychopaths suffered some form of childhood abuse or neglect.) Obviously there's no DSM in the world of PE, so psychopathy might not even be a thing in this world.
Fair enough about Ares, but from the (admittedly little) I know of the Greek pantheon, is that there were plenty of very specific gods. And the one I have in mind is less about embodying chaos and war, and more about embodying ... a fundamental lacking. His role is a smaller one (especially considering the power=followers idea). And while I don't really want to get into a discussion about contemporary psychoanalysis and theory, I think it's a safe bet to say that psychopathy is a simple enough affliction that it could safely exist in PE's fantasy setting.
Thanks for the reply though. Super interesting.